I have a 76 dodge d-100 truck the lights brighten up when I accelarate. I have replaced the alternator a couple of times with no luck. Does anyone have a clue as to why?

I had an issue like this on an old motorcycle, so maybe this will help.

You might check your regulator and rectifier.
The alternator is just a generator, and produces alternating current. Your battery, of course is direct current. In order for it and all your other accessories, including your headlights, to work properly the alternating current electricity must be rectified (converted to DC from AC).

The regulator controls the amount of electricity that comes back to the battery and the rest of your system so you don't experience changing power levels as your engine revs up.

Of course, if these fail they could cook your battery too, so check it.

An easy way to check this out would be to take a digital multimeter and put it on the battery leads and watch the voltage as you start, idle, and rev the truck. Your battery will rest a little above 13 volts. The voltage will sag a bit as it starts. It will run about 14.3 or so volts while running. As it revs, the voltage should not increase very much at all. If it does, check your regulator/rectifier. If these go unfixed, all your electrical components are in danger of seeing too much voltage.

There is also the possibility that your charging system isn't able to get enough current to your headlights to keep them fully light up while the truck is idle, but that would have been solved by the alternator swap you already did.